Telomerase expression is restricted in human cells and so telomeres shorten throughout our lives, providing a tumour suppressor mechanism that limits cell proliferation. As a trade-off, continuous telomere erosion results in replicative senescence and contributes to ageing. Recently, telomerase therapies were proposed as a valid approach to rescue degenerative phenotypes caused by telomere dysfunction. However, systemic effects initiated by short telomeres may prove dominant in limiting tissue renewal in the whole organism. Most of our knowledge of telomere biology derives from mouse models that do not rely on telomere exhaustion for controlling cell proliferation and tissue homeostasis. In order to understand the impact of telomere shortening in natural ageing, we need to investigate animal models that, like humans, have evolved to have telomere length as a cell division clock.